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arXiv:2603.03887

Kinematic budget of quantum correlations

Maaz Khan, Subhadip Mitra

quant-phSubmitted Mar 4, 2026• Announced Mar 5, 2026• 0 citations• Revised Jun 17, 2026 (v2)
v1 · Mar 4, 2026v2 · Jun 17, 2026
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Abstract

The diversity of quantum correlations -- discord, entanglement, steering, and Bell nonlocality -- disappears at the kinematic level of observable second moments. By treating state purity as a finite resource, we introduce a local-unitary-invariant budget that splits these moments into local and nonlocal sectors. This maps quantum systems onto compact, two-dimensional manifolds whose topology is governed by purity and time-reversal symmetry. This dimensional reduction reveals a deep structural link: exceeding classical capacity limits requires the activation of intrinsically time-odd generators, providing a dimension-agnostic guarantee of negative partial transpose (NPT) entanglement. For two qubits, this geometry is analytically solvable; a single boundary isolates classical correlations, while nested regions define thresholds for steering and Bell nonlocality, alongside bounds on non-stabiliser magic. Beyond two qubits, dimensional bottlenecks enforce the kinematic limits on correlations. Because this macroscopic representation is completely determined by global and marginal purities, it bypasses the exponential scaling of full-state tomography. Thus, whenever an $n$-partite state's correlations exceed the classical capacity limits, its NPT entanglement is certified by only $n+1$ purity measurements, with sample complexity independent of Hilbert space dimension. By coarse-graining over gauge-like first moments, this geometry acts as a thermodynamic phase diagram, exposing the hierarchy of quantum resources and their dynamic redistribution under decoherence.

Comments
Total 19 pages with 10 figures and one table. References and clarifications added

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Abstract Quantum correlations extend beyond entanglement and play a central role in quantum information. Quantum discord captures nonclassical correlations that can persist in separable states. We present the first systematic geometric and operational analysis of MICT-discord in two-qubit systems, integrating numerical validation, scaling laws, noise robustness, and resource geometry. We validate MICT-discord against analytic benchmarks, uncover distinct scaling for entangled versus separable classes, and identify a crossover regime where separable states exceed entangled ones in discord, challenging monotonic assumptions. Under depolarizing and amplitude-damping channels, MICT-discord shows channel-dependent resilience, highlighting potential utility for NISQ devices. In contrast, maximally entangled mixed states (MEMS) expose limitations where MICT-discord fails to detect correlations at low purity. Geometric resource analysis delineates the convex hull boundaries of separable states and reveals the clustering of entangled states in high-discordance regions, providing operational thresholds. Overall, MICT-discord emerges as a structured, coherence-sensitive measure with demonstrated strengths in scaling and noise scenarios, alongside clear limitations in mixed-state regimes. Our results establish a reproducible, geometry-informed framework for discord analysis and suggest practical pathways for resource classification and benchmarking in quantum.
Abstract Quantum correlations extend beyond entanglement and play a central role in quantum information. Quantum discord captures nonclassical correlations that can persist in separable states. We present the first systematic geometric and operational analysis of MICT-discord in two-qubit systems, integrating numerical validation, scaling laws, noise robustness, and resource geometry. We validate MICT-discord against analytic benchmarks, uncover distinct scaling for entangled versus separable classes, and identify a crossover regime where separable states exceed entangled ones in discord, challenging monotonic assumptions. Under depolarizing and amplitude-damping channels, MICT-discord shows channel-dependent resilience, highlighting potential utility for NISQ devices. In contrast, maximally entangled mixed states (MEMS) expose limitations where MICT-discord fails to detect correlations at low purity. Geometric resource analysis delineates the convex hull boundaries of separable states and reveals the clustering of entangled states in high-discordance regions, providing operational thresholds. Overall, MICT-discord emerges as a structured, coherence-sensitive measure with demonstrated strengths in scaling and noise scenarios, alongside clear limitations in mixed-state regimes. Our results establish a reproducible, geometry-informed framework for discord analysis and suggest practical pathways for resource classification and benchmarking in quantum.
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Quantum entanglement does not necessarily imply Einstein-Podolsky-Rosen steering. We identify a \emph{boundary mechanism} that closes this gap when an entangled state meets the boundary of the trusted state space in a nondegenerate way. The mechanism is local: a projective assemblage that approaches a boundary contact with first-order tangential coherence but only second-order inward defect cannot be reproduced by any finite-measure local-hidden-state model. In finite dimensions this yields a support-kernel criterion for an arbitrary fixed steering cut: if a trusted conditional state is rank-deficient and its first-order block couples its support to its kernel, then the state is both NPT (negative partial transpose) and projectively steerable. The two-qubit product-null sector provides the minimal transparent realization. A product vector in the kernel gives the pure boundary contact, and a single coherence entry simultaneously serves as the tangential displacement, the NPT minor, and the steering obstruction. Hence, on this boundary, entanglement collapses to two-way projective steering -- including the genuinely mixed rank-three branch and the rank-two case as a low-dimensional instance. We also provide a filtered standard form, an explicit rank-three Cholesky parametrization, and a compact boundary certificate.
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Nonlocality is one of the most important resources for quantum information protocols.The observation of nonlocal correlations in a Bell experiment is the result of appropriately chosen measurements and quantum states.We quantify the minimal purity to achieve a certain Bell value for any Bell operator.Since purity is the most fundamental resource of a quantum state, this enables us also to quantify the necessary coherence, discord, and entanglement for a given violation of two-qubit correlation inequalities.Our results shine a light on the Clauser-Horne-Shimony-Holt inequality by showing that for a fixed Bell violation an increase in the measurement resources does not always lead to a decrease of the minimal state resources.